Decorrelation-Based Feature Discovery: TADPOLE-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

Data from the speech features

1.2 The data set

TADPOLE_D1_D2 <- read.csv("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2.csv")
TADPOLE_D1_D2_Dict <- read.csv("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2_Dict.csv")
TADPOLE_D1_D2_Dict_LR <- as.data.frame(read_excel("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2_Dict_LR.xlsx",sheet = "LeftRightFeatures"))


rownames(TADPOLE_D1_D2_Dict) <- TADPOLE_D1_D2_Dict$FLDNAME

1.3 Conditioning the data

# mm3 to mm
isVolume <- c("Ventricles","Hippocampus","WholeBrain","Entorhinal","Fusiform","MidTemp","ICV",
              TADPOLE_D1_D2_Dict$FLDNAME[str_detect(TADPOLE_D1_D2_Dict$TEXT,"Volume")]
              )


#TADPOLE_D1_D2[,isVolume] <- apply(TADPOLE_D1_D2[,isVolume],2,'^',(1/3))
TADPOLE_D1_D2[,isVolume] <- TADPOLE_D1_D2[,isVolume]^(1/3)

# mm2 to mm
isArea <- TADPOLE_D1_D2_Dict$FLDNAME[str_detect(TADPOLE_D1_D2_Dict$TEXT,"Area")]
TADPOLE_D1_D2[,isArea] <- sqrt(TADPOLE_D1_D2[,isArea])

# Get only cross sectional measurements
FreeSurfersetCross <- str_detect(colnames(TADPOLE_D1_D2),"UCSFFSX")

# The subset of baseline measurements
baselineTadpole <- subset(TADPOLE_D1_D2,VISCODE=="bl")
table(baselineTadpole$DX)

                   Dementia Dementia to MCI             MCI MCI to Dementia 
          7             336               1             864               5 
  MCI to NL              NL       NL to MCI 
          2             521               1 

table(baselineTadpole$DX_bl)

AD CN EMCI LMCI SMC 342 417 310 562 106

rownames(baselineTadpole) <- baselineTadpole$PTID


validBaselineTadpole <- cbind(DX=baselineTadpole$DX_bl,
                                 AGE=baselineTadpole$AGE,
                                 Gender=1*(baselineTadpole$PTGENDER=="Female"),
                                 ADAS11=baselineTadpole$ADAS11,
                                 ADAS13=baselineTadpole$ADAS13,
                                 MMSE=baselineTadpole$MMSE,
                                 RAVLT_immediate=baselineTadpole$RAVLT_immediate,
                                 RAVLT_learning=baselineTadpole$RAVLT_learning,
                                 RAVLT_forgetting=baselineTadpole$RAVLT_forgetting,
                                 RAVLT_perc_forgetting=baselineTadpole$RAVLT_perc_forgetting,
                                 FAQ=baselineTadpole$FAQ,
                                 Ventricles=baselineTadpole$Ventricles,
                                 Hippocampus=baselineTadpole$Hippocampus,
                                 WholeBrain=baselineTadpole$WholeBrain,
                                 Entorhinal=baselineTadpole$Entorhinal,
                                 Fusiform=baselineTadpole$Fusiform,
                                 MidTemp=baselineTadpole$MidTemp,
                                 ICV=baselineTadpole$ICV,
                                 baselineTadpole[,FreeSurfersetCross])


LeftFields <- TADPOLE_D1_D2_Dict_LR$LFN
names(LeftFields) <- LeftFields
LeftFields <- LeftFields[LeftFields %in% colnames(validBaselineTadpole)]
RightFields <- TADPOLE_D1_D2_Dict_LR$RFN
names(RightFields) <- RightFields
RightFields <- RightFields[RightFields %in% colnames(validBaselineTadpole)]

## Normalize to ICV
validBaselineTadpole$Ventricles=validBaselineTadpole$Ventricles/validBaselineTadpole$ICV
validBaselineTadpole$Hippocampus=validBaselineTadpole$Hippocampus/validBaselineTadpole$ICV
validBaselineTadpole$WholeBrain=validBaselineTadpole$WholeBrain/validBaselineTadpole$ICV
validBaselineTadpole$Entorhinal=validBaselineTadpole$Entorhinal/validBaselineTadpole$ICV
validBaselineTadpole$Fusiform=validBaselineTadpole$Fusiform/validBaselineTadpole$ICV
validBaselineTadpole$MidTemp=validBaselineTadpole$MidTemp/validBaselineTadpole$ICV

leftData <- validBaselineTadpole[,LeftFields]/validBaselineTadpole$ICV
RightData <- validBaselineTadpole[,RightFields]/validBaselineTadpole$ICV

## get mean and relative difference 
meanLeftRight <- (leftData + RightData)/2
difLeftRight <- abs(leftData - RightData)
reldifLeftRight <- difLeftRight/meanLeftRight
colnames(meanLeftRight) <- paste("M",colnames(meanLeftRight),sep="_")
colnames(difLeftRight) <- paste("D",colnames(difLeftRight),sep="_")
colnames(reldifLeftRight) <- paste("RD",colnames(reldifLeftRight),sep="_")


validBaselineTadpole <- validBaselineTadpole[,!(colnames(validBaselineTadpole) %in% 
                                               c(LeftFields,RightFields))]
validBaselineTadpole <- cbind(validBaselineTadpole,meanLeftRight,difLeftRight,reldifLeftRight)
#validBaselineTadpole <- cbind(validBaselineTadpole,meanLeftRight,difLeftRight)
#validBaselineTadpole <- cbind(validBaselineTadpole,leftData,RightData)

## Remove columns with too many NA more than %15 of NA
nacount <- apply(is.na(validBaselineTadpole),2,sum)/nrow(validBaselineTadpole) < 0.15
diagnose <- validBaselineTadpole$DX
pander::pander(table(diagnose))

AD	CN	EMCI	LMCI	SMC
342	417	310	562	106

validBaselineTadpole <- validBaselineTadpole[,nacount]
## Remove character columns
ischar <- sapply(validBaselineTadpole,class) == "character"
validBaselineTadpole <- validBaselineTadpole[,!ischar]
## Place back diagnose
validBaselineTadpole$DX <- diagnose


validBaselineTadpole <- validBaselineTadpole[complete.cases(validBaselineTadpole),]
ischar <- sapply(validBaselineTadpole,class) == "character"
validBaselineTadpole[,!ischar] <- sapply(validBaselineTadpole[,!ischar],as.numeric)

colnames(validBaselineTadpole) <- str_remove_all(colnames(validBaselineTadpole),"_UCSFFSX_11_02_15_UCSFFSX51_08_01_16")
colnames(validBaselineTadpole) <- str_replace_all(colnames(validBaselineTadpole)," ","_")
validBaselineTadpole$LONISID <- NULL
validBaselineTadpole$IMAGEUID <- NULL
validBaselineTadpole$LONIUID <- NULL

diagnose <- as.character(validBaselineTadpole$DX)
validBaselineTadpole$DX <- diagnose
pander::pander(table(validBaselineTadpole$DX))

AD	CN	EMCI	LMCI	SMC
245	359	272	444	93

validBaselineTadpole[validBaselineTadpole$DX %in% c("EMCI","LMCI"),"DX"] <- "MCI" 
validBaselineTadpole[validBaselineTadpole$DX %in% c("CN","SMC"),"DX"] <- "NL" 

pander::pander(table(validBaselineTadpole$DX))

AD	MCI	NL
245	716	452

1.4 Get the Time To Event on MCI Subjects

subjectsID <- rownames(validBaselineTadpole)
visitsID <- unique(TADPOLE_D1_D2$VISCODE)
baseDx <- TADPOLE_D1_D2[TADPOLE_D1_D2$VISCODE=="bl",c("PTID","DX","EXAMDATE")]
rownames(baseDx) <- baseDx$PTID 
baseDx <- baseDx[subjectsID,]
lastDx <- baseDx
toDementia <- baseDx
table(lastDx$DX)

   Dementia Dementia to MCI             MCI MCI to Dementia       MCI to NL 
        244               1             711               2               2 
         NL       NL to MCI 
        452               1 

hasDementia <- lastDx$PTID[str_detect(lastDx$DX,"Dementia")]


for (vid in visitsID)
{
  DxValue <- TADPOLE_D1_D2[TADPOLE_D1_D2$VISCODE==vid,c("PTID","DX","EXAMDATE")]
  rownames(DxValue) <- DxValue$PTID 
  DxValue <- DxValue[DxValue$PTID %in% subjectsID,]
  noDX <- DxValue$PTID[nchar(DxValue$DX) < 1]
  print(length(noDX))
  DxValue[noDX,] <- lastDx[noDX,]
  inLast <- lastDx$PTID[lastDx$PTID %in% DxValue$PTID]
  print(length(inLast))
  lastDx[inLast,] <- DxValue[inLast,]
  noDementia <- !(toDementia$PTID %in% hasDementia)
  toDementia[noDementia,] <- lastDx[noDementia,]
  hasDementia <- unique(c(hasDementia,lastDx$PTID[str_detect(lastDx$DX,"Dementia")]))
}

[1] 0 [1] 1413 [1] 2 [1] 1326 [1] 6 [1] 1218 [1] 23 [1] 1095 [1] 805 [1] 1058 [1] 29 [1] 710 [1] 20 [1] 212 [1] 14 [1] 167 [1] 32 [1] 553 [1] 25 [1] 298 [1] 18 [1] 130 [1] 667 [1] 667 [1] 112 [1] 112 [1] 176 [1] 176 [1] 177 [1] 177 [1] 625 [1] 625 [1] 251 [1] 251 [1] 159 [1] 159 [1] 7 [1] 7 [1] 17 [1] 99 [1] 9 [1] 63 [1] 1 [1] 1

table(lastDx$DX)

   Dementia Dementia to MCI             MCI MCI to Dementia       MCI to NL 
        428               2             463              80               7 
         NL  NL to Dementia       NL to MCI 
        406               1              26 

baseMCI <-baseDx$PTID[baseDx$DX == "MCI"]
lastDementia <- lastDx$PTID[str_detect(lastDx$DX,"Dementia")]
lastDementia2 <- toDementia$PTID[str_detect(toDementia$DX,"Dementia")]
lastNL <- lastDx$PTID[str_detect(lastDx$DX,"NL")]

MCIatBaseline <- baseDx[baseMCI,]
MCIatEvent <- toDementia[baseMCI,]
MCIatLast <- lastDx[baseMCI,]

MCIconverters <- MCIatBaseline[baseMCI %in% lastDementia,]
MCI_No_converters <- MCIatBaseline[!(baseMCI %in% MCIconverters$PTID),]
MCIconverters$TimeToEvent <- (as.Date(toDementia[MCIconverters$PTID,"EXAMDATE"]) 
                                   - as.Date(MCIconverters$EXAMDATE))

sum(MCIconverters$TimeToEvent ==0)

[1] 0

MCIconverters$AtEventDX <- MCIatEvent[MCIconverters$PTID,"DX"]
MCIconverters$LastDX <- MCIatLast[MCIconverters$PTID,"DX"]

MCI_No_converters$TimeToEvent <- (as.Date(lastDx[MCI_No_converters$PTID,"EXAMDATE"]) 
                                   - as.Date(MCI_No_converters$EXAMDATE))

MCI_No_converters$LastDX <- MCIatLast[MCI_No_converters$PTID,"DX"]

MCI_No_converters <- subset(MCI_No_converters,TimeToEvent > 0)

2 Prognosis MCI to AD Conversion

2.1 the set

MCIPrognosisIDs <- c(MCIconverters$PTID,MCI_No_converters$PTID)

TADPOLECrossMRI <- validBaselineTadpole[MCIPrognosisIDs,]
table(TADPOLECrossMRI$DX)

MCI 680

TADPOLECrossMRI$DX <- NULL
TADPOLECrossMRI$status <- 1*(rownames(TADPOLECrossMRI) %in% MCIconverters$PTID)
table(TADPOLECrossMRI$status)

0 1 436 244

2.1.0.1 Standarize the names for the reporting

studyName <- "TADPOLE"
dataframe <- TADPOLECrossMRI
outcome <- "status"

TopVariables <- 10

thro <- 0.60
cexheat = 0.15

2.2 Generaring the report

2.2.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

2.2.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
680	477

pander::pander(table(dataframe[,outcome]))

0	1
436	244

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

2.2.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

2.3 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

2.3.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9996707

2.4 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 476 , Uni p: 0.0005252101 , Outcome-Driven Size: 0 , Base Size: 167 , Rcrit: 0.1253887 
#> 
#> 
 1 <R=1.000,thr=0.900>, Top: 156( 1 ).[ 1 : 156 Fa= 156 : 0.900 ]( 156 , 156 , 0 ),<|>Tot Used: 312 , Added: 156 , Zero Std: 0 , Max Cor: 0.884
#> 
 2 <R=0.884,thr=0.750>, Top: 101( 1 ).[ 1 : 101 Fa= 240 : 0.750 ]( 101 , 135 , 156 ),<|>Tot Used: 431 , Added: 135 , Zero Std: 0 , Max Cor: 0.913
#> 
 3 <R=0.913,thr=0.900>, Top: 2( 1 )[ 1 : 2 Fa= 240 : 0.900 ]( 2 , 2 , 240 ),<|>Tot Used: 431 , Added: 2 , Zero Std: 0 , Max Cor: 0.872
#> 
 4 <R=0.872,thr=0.750>, Top: 12( 1 )[ 1 : 12 Fa= 248 : 0.750 ]( 12 , 16 , 240 ),<|>Tot Used: 443 , Added: 16 , Zero Std: 0 , Max Cor: 0.877
#> 
 5 <R=0.877,thr=0.750>, Top: 2( 1 )[ 1 : 2 Fa= 250 : 0.750 ]( 2 , 2 , 248 ),<|>Tot Used: 443 , Added: 2 , Zero Std: 0 , Max Cor: 0.750
#> 
 6 <R=0.750,thr=0.600>, Top: 42( 1 )[ 1 : 42 Fa= 266 : 0.600 ]( 42 , 89 , 250 ),<|>Tot Used: 464 , Added: 89 , Zero Std: 0 , Max Cor: 0.953
#> 
 7 <R=0.953,thr=0.900>, Top: 1( 1 )[ 1 : 1 Fa= 266 : 0.900 ]( 1 , 1 , 266 ),<|>Tot Used: 464 , Added: 1 , Zero Std: 0 , Max Cor: 0.880
#> 
 8 <R=0.880,thr=0.750>, Top: 6( 1 )[ 1 : 6 Fa= 266 : 0.750 ]( 6 , 6 , 266 ),<|>Tot Used: 465 , Added: 6 , Zero Std: 0 , Max Cor: 0.901
#> 
 9 <R=0.901,thr=0.900>, Top: 1( 1 )[ 1 : 1 Fa= 266 : 0.900 ]( 1 , 1 , 266 ),<|>Tot Used: 465 , Added: 1 , Zero Std: 0 , Max Cor: 0.849
#> 
 10 <R=0.849,thr=0.750>, Top: 1( 1 )[ 1 : 1 Fa= 266 : 0.750 ]( 1 , 1 , 266 ),<|>Tot Used: 465 , Added: 1 , Zero Std: 0 , Max Cor: 0.750
#> 
 11 <R=0.750,thr=0.600>, Top: 22( 1 )[ 1 : 22 Fa= 271 : 0.600 ]( 22 , 27 , 266 ),<|>Tot Used: 469 , Added: 27 , Zero Std: 0 , Max Cor: 0.844
#> 
 12 <R=0.844,thr=0.750>, Top: 5( 1 )[ 1 : 5 Fa= 274 : 0.750 ]( 5 , 5 , 271 ),<|>Tot Used: 469 , Added: 5 , Zero Std: 0 , Max Cor: 0.874
#> 
 13 <R=0.874,thr=0.750>, Top: 1( 1 )[ 1 : 1 Fa= 274 : 0.750 ]( 1 , 1 , 274 ),<|>Tot Used: 469 , Added: 1 , Zero Std: 0 , Max Cor: 0.739
#> 
 14 <R=0.739,thr=0.600>, Top: 10( 2 )[ 1 : 10 Fa= 277 : 0.600 ]( 9 , 12 , 274 ),<|>Tot Used: 469 , Added: 12 , Zero Std: 0 , Max Cor: 0.914
#> 
 15 <R=0.914,thr=0.900>, Top: 1( 1 )[ 1 : 1 Fa= 277 : 0.900 ]( 1 , 1 , 277 ),<|>Tot Used: 469 , Added: 1 , Zero Std: 0 , Max Cor: 0.833
#> 
 16 <R=0.833,thr=0.750>, Top: 2( 1 )[ 1 : 2 Fa= 277 : 0.750 ]( 2 , 2 , 277 ),<|>Tot Used: 469 , Added: 2 , Zero Std: 0 , Max Cor: 0.720
#> 
 17 <R=0.720,thr=0.600>, Top: 3( 1 )[ 1 : 3 Fa= 278 : 0.600 ]( 3 , 3 , 277 ),<|>Tot Used: 469 , Added: 3 , Zero Std: 0 , Max Cor: 0.742
#> 
 18 <R=0.742,thr=0.600>, Top: 1( 1 )[ 1 : 1 Fa= 278 : 0.600 ]( 1 , 1 , 278 ),<|>Tot Used: 469 , Added: 1 , Zero Std: 0 , Max Cor: 0.599
#> 
 19 <R=0.599,thr=0.600>
#> 
 [ 19 ], 0.5993343 Decor Dimension: 469 Nused: 469 . Cor to Base: 258 , ABase: 161 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

1378

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

430

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

0.827

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

0.535

2.4.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

2.5 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

2.6 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.5993343

2.7 U-MAP Visualization of features

2.7.1 The UMAP based on LASSO on Raw Data

if (nrow(dataframe) < 1000)
{
  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}

2.7.2 The decorralted UMAP

if (nrow(dataframe) < 1000)
{

  datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}

2.8 Univariate Analysis

2.8.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : M_ST24SA 200 : D_ST49TA 300 : D_ST47CV 400 : RD_ST24SA

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : M_ST24SA 200 : D_ST49TA 300 : La_D_ST47CV 400 : La_RD_ST24SA

2.8.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
ADAS13	20.7611	6.16923	14.0091	5.78970	0.03549	0.788
ADAS11	12.8635	4.56128	8.7155	3.84978	0.00264	0.761
FAQ	5.4631	4.90262	1.9266	2.98257	0.00000	0.756
M_ST40CV	0.1799	0.00875	0.1875	0.00763	0.28199	0.750
M_ST29SV	0.1253	0.00708	0.1321	0.00750	0.58088	0.745
M_ST12SV	0.0913	0.00535	0.0962	0.00550	0.50030	0.744
Hippocampus	0.1582	0.00886	0.1664	0.00945	0.44340	0.737
RAVLT_immediate	29.0205	7.69236	37.2798	10.92838	0.04406	0.728
M_ST24CV	0.0996	0.00800	0.1059	0.00706	0.04673	0.727
M_ST31CV	0.1910	0.00945	0.1986	0.00902	0.94566	0.717

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
ADAS13	2.08e+01	6.169227	14.00911	5.789699	3.55e-02	0.788
FAQ	5.46e+00	4.902619	1.92661	2.982574	0.00e+00	0.756
Hippocampus	1.58e-01	0.008856	0.16644	0.009452	4.43e-01	0.737
La_RD_ST12SV	4.99e-04	0.003050	-0.00119	0.003038	1.28e-12	0.697
M_ST13CV	1.09e-01	0.005870	0.11310	0.005687	4.34e-01	0.690
La_M_ST44TA	6.98e-03	0.000922	0.00762	0.001055	8.04e-02	0.684
La_RD_ST32TA	1.02e-03	0.008440	-0.00273	0.005438	6.65e-07	0.679
M_ST59TA	1.95e-02	0.001788	0.02060	0.001722	2.16e-01	0.679
La_RD_ST24CV	5.65e-04	0.008607	-0.00303	0.005685	5.67e-08	0.675
M_ST55CV	2.01e-01	0.008959	0.20618	0.008053	6.16e-01	0.674
La_RD_ST36CV	2.31e-04	0.001140	-0.00031	0.000969	6.94e-07	0.673

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.76	276	0.579

theCharformulas <- attr(dc,"LatentCharFormulas")


finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores
ADAS13	NA	2.08e+01	6.169227	14.00911	5.79e+00	3.55e-02	0.788	0.788	2
ADAS131	NA	2.08e+01	6.169227	14.00911	5.79e+00	3.55e-02	0.788	NA	NA
ADAS11	NA	1.29e+01	4.561284	8.71553	3.85e+00	2.64e-03	0.761	0.761	NA
FAQ	NA	5.46e+00	4.902619	1.92661	2.98e+00	0.00e+00	0.756	0.756	NA
FAQ1	NA	5.46e+00	4.902619	1.92661	2.98e+00	0.00e+00	0.756	NA	NA
M_ST40CV	NA	1.80e-01	0.008748	0.18753	7.63e-03	2.82e-01	0.750	0.750	NA
M_ST29SV	NA	1.25e-01	0.007075	0.13210	7.50e-03	5.81e-01	0.745	0.745	NA
M_ST12SV	NA	9.13e-02	0.005353	0.09622	5.50e-03	5.00e-01	0.744	0.744	NA
Hippocampus	NA	1.58e-01	0.008856	0.16644	9.45e-03	4.43e-01	0.737	0.737	7
Hippocampus1	NA	1.58e-01	0.008856	0.16644	9.45e-03	4.43e-01	0.737	NA	NA
RAVLT_immediate	NA	2.90e+01	7.692361	37.27982	1.09e+01	4.41e-02	0.728	0.728	NA
M_ST24CV	NA	9.96e-02	0.008002	0.10594	7.06e-03	4.67e-02	0.727	0.727	NA
M_ST31CV	NA	1.91e-01	0.009453	0.19857	9.02e-03	9.46e-01	0.717	0.717	NA
La_RD_ST12SV	- (10.875)D_ST12SV + RD_ST12SV	4.99e-04	0.003050	-0.00119	3.04e-03	1.28e-12	0.697	0.552	-1
M_ST13CV	NA	1.09e-01	0.005870	0.11310	5.69e-03	4.34e-01	0.690	0.690	2
La_M_ST44TA	+ M_ST44TA + (0.141)M_ST44SA - (0.425)M_ST44CV	6.98e-03	0.000922	0.00762	1.05e-03	8.04e-02	0.684	0.658	-1
La_RD_ST32TA	- (44.617)D_ST32TA + RD_ST32TA	1.02e-03	0.008440	-0.00273	5.44e-03	6.65e-07	0.679	0.564	0
M_ST59TA	NA	1.95e-02	0.001788	0.02060	1.72e-03	2.16e-01	0.679	0.679	54
La_RD_ST24CV	- (10.055)D_ST24CV + RD_ST24CV	5.65e-04	0.008607	-0.00303	5.69e-03	5.67e-08	0.675	0.560	-1
M_ST55CV	NA	2.01e-01	0.008959	0.20618	8.05e-03	6.16e-01	0.674	0.674	4
La_RD_ST36CV	- (6.247)D_ST36CV + RD_ST36CV	2.31e-04	0.001140	-0.00031	9.69e-04	6.94e-07	0.673	0.514	-1

2.9 Comparing IDeA vs PCA vs EFA

2.9.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

2.9.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

2.10 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	330	106
1	36	208

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.791	0.759	0.821
3	se	0.852	0.802	0.894
4	sp	0.757	0.714	0.796
6	diag.or	17.987	11.866	27.267

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	327	109
1	38	206

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.784	0.751	0.814
3	se	0.844	0.793	0.887
4	sp	0.750	0.707	0.790
6	diag.or	16.263	10.811	24.465

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	398	38
1	134	110

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.747	0.713	0.779
3	se	0.451	0.387	0.516
4	sp	0.913	0.882	0.938
6	diag.or	8.598	5.663	13.053

par(op)

2.10.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	364	72
1	83	161

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.772	0.739	0.803
3	se	0.660	0.597	0.719
4	sp	0.835	0.797	0.868
6	diag.or	9.807	6.800	14.142

  par(op)